Lecture 0 (01/08)
Definitions: Categories. Morphisms - injective, surjective, bijective, left/right inverse, isomorphisms. Objects - sub/quotient, initial/final, null.
Lecture 1 (01/10)
Functors. Natural transformations. Equivalence of categories.
Lecture 2 (01/12)
Equivalence of categories cntd. Dual categories. Product of catgories.
There is a mistake in Lecture 2. See section 3.0 of the next lecture for errata
Lecture 3 (01/17)
Adjoint functors. Unit and counit of adjunction.
Lecture 4 (01/19)
Adjoint functors cntd. Yoneda's lemma. Representable functors.
Lecture 5 (01/22)
(Functors defining objects). Direct sums and direct products.
Lecture 6 (01/24)
(Functors defining objects). Inverse limit.
Lecture 7 (01/26)
Direct and inverse limits cntd.
Lecture 8 (01/29)
Additive categories. Finite direct sums/products. Kernel and cokernel.
Lecture 9 (01/31)
Kernel and cokernel continued. Abelian categories. Additive functors.
Lecture 10 (02/02)
Notion of exactness: of sequences; of functors. Left/right exact functors. Hom functor.
Lecture 11 (02/05)
Long road ahead - towards derived functors. To do list.
Lecture 12 (02/07)
Injective and projective objects - "effacability".
Lecture 13 (02/09)
Tensor functor. Right exactness.
Lecture 14 (02/12)
Category of complexes. Cohomology functors. Snake lemma.
Lecture 15 (02/14)
Long exact sequence in cohomology. Homotopy.
Lecture 16 (02/16)
Uniqueness (up to homotopy) of injective and projective resolutions.
Optional reading material
Grothendieck's axioms (AB3-5) and proof of Baer's criterion of injectivity